Hölder regularity for metric Anosov flows

We define a class of flows on compact metric spaces that we call \emph{$C^α$ metric Anosov flows}, $0 < α< 1$ or $α= \mathrm{Lip}$. We give verifiable criteria for a metric Anosov flow to be $C^α$. We show that $C^α$ metric Anosov flows have Hölder continuous local product structure, and in particul